Subgroups — #15756678

Order 3328.

362 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13114952	C₂	1	2	yes	maximal
2	#13114581	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718050	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718072	C₂	1	2	yes	maximal
5	C₂×C₁₃×#335	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊#1055	C₂²	1	2	yes	—
10	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
11	C₁₃×#335	—	2	2	no	—
12	#11718142	—	2	4	no	—
13	#11718142	C₄	1	2	yes	—
14	#11718142	C₄	1	2	yes	—
15	#11718072	—	2	4	no	—
16	#11718050	—	2	2	no	—
17	C₂²×C₈×C₁₃	—	2	2	no	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
21	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
23	C₂×C₄×Dic₁₃	Q₈	1	2	yes	—
24	C₂²×#1055	—	2	2	no	—
25	C₂²×#1055	C₂×C₄	1	2	yes	—
26	C₁₃×C₄⋊C₈	—	2	2	no	—
27	C₁₃×C₄⋊C₈	—	2	2	no	—
28	C₄×C₈×C₁₃	D₄	1	2	yes	—
29	C₄×C₈×C₁₃	Q₈	1	2	yes	—
30	C₄⋊#1055	—	2	2	no	—
31	C₄⋊#1055	—	2	2	no	—
32	C₄×#1055	D₄	1	2	yes	—
33	C₄×#1055	Q₈	1	2	yes	—
34	#8811	—	13	1	no	maximal, Sylow
35	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
38	C₂²×Dic₁₃	C₄⋊C₄	1	4	yes	—
39	C₂×C₈×C₁₃	—	2	2	no	—
40	C₂×C₈×C₁₃	—	2	2	no	—
41	C₂×C₈×C₁₃	—	4	2	no	—
42	C₂×C₈×C₁₃	—	4	4	no	—
43	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
44	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
45	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
48	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
49	C₄×Dic₁₃	—	2	2	no	—
50	C₄×Dic₁₃	—	2	2	no	—
51	C₄×Dic₁₃	—	2	2	no	—
52	C₄×Dic₁₃	—	2	2	no	—
53	C₄×Dic₁₃	—	4	2	no	—
54	C₂×#1055	—	2	2	no	—
55	C₂×#1055	—	2	2	no	—
56	C₂×#1055	—	4	2	no	—
57	C₂×#1055	—	4	4	no	—
58	C₂×#1055	C₄⋊C₄	1	4	yes	—
59	#1831	—	13	2	no	—
60	#1744	—	13	1	no	—
61	C₂×#335	—	13	1	no	—
62	C₂×#335	D₁₃	1	1	yes	characteristic
63	C₂×#334	—	13	2	no	—
64	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₃	—	2	2	no	—
66	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₄×C₁₃	#131	1	2	yes	—
73	C₂×C₄×C₁₃	#131	1	2	yes	—
74	C₂×C₄×C₁₃	#135	1	2	yes	—
75	C₂×C₄×C₁₃	#135	1	2	yes	—
76	C₂×Dic₁₃	—	2	4	no	—
77	C₂×Dic₁₃	—	2	4	no	—
78	C₂×Dic₁₃	—	2	4	no	—
79	C₈×C₁₃	—	2	2	no	—
80	C₈×C₁₃	—	2	2	no	—
81	C₈×C₁₃	—	8	2	no	—
82	#1055	—	2	4	no	—
83	#1055	—	8	2	no	—
84	C₂×C₄⋊C₈	—	13	2	no	—
85	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
86	C₂×C₄×C₈	—	13	1	no	—
87	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
88	C₄³	—	13	1	no	—
89	#336	—	13	2	no	—
90	#336	—	13	2	no	—
91	#336	—	26	4	no	—
92	#335	—	2	2	no	—
93	#335	—	26	2	no	—
94	#334	—	26	4	no	—
95	C₂²×C₁₃	#384	1	1	yes	characteristic
96	C₂²×C₁₃	#424	1	2	yes	—
97	C₂²×C₁₃	#427	1	2	yes	—
98	C₂²×C₁₃	#430	1	2	yes	—
99	C₄×C₁₃	—	2	1	no	—
100	C₄×C₁₃	—	2	1	no	—
101	C₄×C₁₃	#424	1	2	yes	—
102	C₄×C₁₃	#424	1	1	yes	characteristic
103	C₄×C₁₃	#424	1	1	yes	characteristic
104	C₄×C₁₃	#495	1	1	yes	characteristic
105	C₄×C₁₃	#495	1	1	yes	characteristic
106	C₄×C₁₃	#499	1	2	yes	—
107	Dic₁₃	—	4	4	no	—
108	C₂²×C₈	—	2	2	no	—
109	C₂²×C₈	—	13	2	no	—
110	C₂²×C₈	—	26	2	no	—
111	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
112	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
113	C₂×C₄²	—	13	2	no	—
114	C₂×C₄²	—	13	2	no	—
115	C₂×C₄²	—	13	2	no	—
116	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
117	C₄⋊C₈	—	2	2	no	—
118	C₄⋊C₈	—	2	2	no	—
119	C₄⋊C₈	—	26	2	no	—
120	C₄⋊C₈	—	26	2	no	—
121	C₄×C₈	—	13	2	no	—
122	C₄×C₈	—	13	2	no	—
123	C₄×C₈	Dic₂₆	1	2	yes	—
124	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
125	C₂×C₁₃	#1572	1	4	yes	—
126	C₂×C₁₃	#1843	1	1	yes	characteristic
127	C₂×C₁₃	#1846	1	1	yes	characteristic
128	C₂×C₁₃	#1849	1	1	yes	characteristic
129	C₂²×C₄	—	13	4	no	—
130	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
131	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
132	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
133	C₂×C₈	—	2	2	no	—
134	C₂×C₈	—	2	2	no	—
135	C₂×C₈	—	4	4	no	—
136	C₂×C₈	—	4	2	no	—
137	C₂×C₈	—	13	4	no	—
138	C₂×C₈	—	26	2	no	—
139	C₂×C₈	—	26	2	no	—
140	C₂×C₈	—	52	4	no	—
141	C₂×C₈	—	52	2	no	—
142	C₂×C₈	#6101	1	2	yes	—
143	C₂×C₈	#6101	1	2	yes	—
144	C₄²	—	26	2	no	—
145	C₄²	—	26	2	no	—
146	C₄²	—	26	2	no	—
147	C₄²	—	26	2	no	—
148	C₄²	—	52	2	no	—
149	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
150	C₄²	D₄×D₁₃	1	1	yes	characteristic
151	C₄²	Q₈×D₁₃	1	1	yes	characteristic
152	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
153	C₁₃	#8811	1	1	yes	characteristic, complemented, Sylow
154	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	26	4	no	—
157	C₂×C₄	—	26	4	no	—
158	C₂×C₄	—	26	4	no	—
159	C₂×C₄	#88142	1	1	yes	characteristic
160	C₂×C₄	#88142	1	1	yes	characteristic
161	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
162	C₂×C₄	#88155	1	2	yes	—
163	C₂×C₄	#88161	1	2	yes	—
164	C₂×C₄	#88166	1	2	yes	—
165	C₂×C₄	#88173	1	2	yes	—
166	C₂×C₄	C₂×#6101	1	1	yes	characteristic
167	C₂×C₄	#88194	1	1	yes	characteristic
168	C₂×C₄	#88198	1	1	yes	characteristic
169	C₈	—	2	2	no	—
170	C₈	—	2	2	no	—
171	C₈	—	8	2	no	—
172	C₈	—	26	4	no	—
173	C₈	—	104	2	no	—
174	C₂²	#11718500	1	2	yes	—
175	C₂²	#11718541	1	2	yes	—
176	C₂²	#11718554	1	2	yes	—
177	C₂²	#11718637	1	1	yes	characteristic
178	C₄	—	2	1	no	—
179	C₄	—	2	1	no	—
180	C₄	—	52	4	no	—
181	C₄	#11718500	1	2	yes	—
182	C₄	#11718539	1	2	yes	—
183	C₄	#11718763	1	1	yes	characteristic
184	C₄	#11718780	1	1	yes	characteristic
185	C₄	#11718816	1	1	yes	characteristic
186	C₄	#11718852	1	1	yes	characteristic
187	C₂	#13113615	1	4	yes	—
188	C₂	#13114989	1	1	yes	characteristic
189	C₂	#13114999	1	1	yes	characteristic
190	C₂	#13115009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#335	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×#335	D₁₃
hypocenter	C₁₃	#8811
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
153. C₁₃	#8811	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13114952	2
#13114581	2
C₂×#11718050	2
C₂×#11718072	2
C₂×C₁₃×#335	2
#8811	13